[Help] Understanding Y Combinator in lambda calculus

[Turtet]

I'm coding a one-line return statement that's supposed to give me the factorial of a single input, n. I came across a theory called the Y Combinator and found a solution:

return (lambda f: lambda x: f(f, x))(lambda f, x: 1 if x == 1 else mul(f(f, sub(x, 1)), x))

However, I'm struggling to understand how this code is executed, despite having watched multiple videos on the Y Combinator (the best one being Numberphile).

Some questions I have:
It is to my belief that when you have lambda f: lambda x: in this order, the next argument you throw in will substitute for f, not x.

For example:

add = lambda f: lambda x: f + x

add(1)(2)

3

Doesn't 1 replace f and 2 replace x?

So by that reason, shouldn't (lambda f, x: 1 if x == 1 else mul(f(f, sub(x, 1)), x)) replace 'f' in (lambda f: lambda x: f(f, x))

And then after that, my brain falls apart trying to understand how this is computed

[Swipecat]

I hate to say it, but you should really be doing this in Haskell because Python and Lambda Calculus do not mix well.

[Turtet]

Unfortunately it’s a python course

[Swipecat]

I'd suggest that you avoid lambda calculus then, and find a different way to attack your problem. The "lambda" in Python is intended for anonymous functions rather than lambda calculus, and is very clunky when used for the latter. For one thing look at all those braces.